Picosecond scale experimental verification of a globally convergent algorithm for a coefficient inverse problem

  title={Picosecond scale experimental verification of a globally convergent algorithm for a coefficient inverse problem},
  author={Michael V. Klibanov and Michael A. Fiddy and Larisa Beilina and Natee Pantong and John O. Schenk},
  journal={Inverse Problems},
A globally convergent algorithm by the first and third authors for a 3D hyperbolic coefficient inverse problem is verified on experimental data measured in the picosecond scale regime. Quantifiable images of dielectric abnormalities are obtained. The total measurement timing of a 100 ps pulse for one detector location was 1.2 ns with 20 ps (=0.02 ns) time step between two consecutive readings. Blind tests have consistently demonstrated an accurate imaging of refractive indexes of dielectric… 

Figures and Tables from this paper

A globally convergent numerical method for a 3D coefficient inverse problem with a single measurement of multi-frequency data
The goal of this paper is to reconstruct spatially distributed dielectric constants from complex-valued scattered wave field by solving a 3D coefficient inverse problem for the Helmholtz equation at
Reconstruction of the Refractive Index from Experimental Backscattering Data Using a Globally Convergent Inverse Method
The goal of this paper is to analyze the performance of the globally convergent algorithm of Beilina and Klibanov on experimental data collected using a microwave scattering facility at the University of North Carolina at Charlotte.
A globally convergent method for a 3-D inverse medium problem for the generalized Helmholtz equation
A 3-D inverse medium problem in the frequency domain is considered. Another name for this problem is Coefficient Inverse Problem. The goal is to reconstruct spatially distributed dielectric constants
Globally Convergent Inverse Reconstruction Algorithms for Detection and Identification of IEDs via Imaging of Spatially Distributed Dielectric Constants Using Microwaves
This grant was given for the period of nine months. The goal of this funding was to verify experimentally the ability of a quantifiable imaging of dielectrics by the new globally convergent inverse
Optical imaging of phantoms from real data by an approximately globally convergent inverse algorithm
The so-called ‘approximate global convergence’ property of this method is shown here and the performance of the algorithm is verified on real data for Diffusion Optical Tomography.
Imaging of buried objects from multi-frequency experimental data using a globally convergent inversion method
Abstract This paper is concerned with the numerical solution to a three-dimensional coefficient inverse problem for buried objects with multi-frequency experimental data. The measured data, which are
Quantitative Image Recovery From Measured Blind Backscattered Data Using a Globally Convergent Inverse Method
The goal of this paper is to introduce the application of a globally convergent inverse scattering algorithm to estimate dielectric constants of targets using time-resolved backscattering data
The adaptivity refines approximate solutions of ill-posed problems due to the relaxation property
Adaptive Finite Element Method (adaptivity) is known to be an effective numerical tool for some ill-posed problems. The key advantage of the adaptivity is the image improvement with local mesh
Relaxation property of the adaptivity technique for some ill-posed problems
A rigorous proof of the adaptivity is presented of the image improvement with local mesh refinements and a good approximation of the exact coefficient without an advanced knowledge of a small neighborhood of that coefficient is delivered.


Direct Reconstructions of Conductivities from Boundary Measurements
A new numerical reconstruction method is presented that solves the nonlinear problem directly without iteration and is extended by introducing a new regularization scheme, which is analyzed theoretically and tested on symmetric and nonsymmetric numerical examples containing computer simulated noise.
Solution of the three-dimensional acoustic inverse scattering problem. The modified Novikov algorithm
For the first time, three-dimensional model scatterers of various strengths and size are numerically reconstructed on the basis of the monochromatic functional-analytical Novikov algorithm. The
MUSIC-Type Electromagnetic Imaging of a Collection of Small Three-Dimensional Inclusions
In this paper we consider the localization of a collection of small, three-dimensional bounded homogeneous inclusions via time-harmonic electromagnetic means, typically using arrays of electric or
GUEST EDITORS' INTRODUCTION: Testing inversion algorithms against experimental data: 3D targets
One of the strengths of Institut Fresnel in Marseille, France, is the tight coupling which exists between experiments and theory. This is how the idea came about, inspired by the Ipswich database
Adaptivity with relaxation for ill-posed problems and global convergence for a coefficient inverse problem
A new framework of the functional analysis is developed for the finite element adaptive method (adaptivity) for the Tikhonov regularization functional for some ill-posed problems. As a result, the
Inverse problems for a perturbed dissipative half-space
Addresses the scattering of acoustic and electromagnetic waves from a perturbed dissipative half-space. For simplicity, the perturbation is assumed to have compact support. Section 1 discusses the
Scattering transformation at fixed non-zero energy for the two-dimensional Schrödinger operator with potential decaying at infinity
We study the problem of reconstructing the potential of the two-dimensional Schrodinger operator from scattering data measured at fixed energy. This problem, in contrast to the general
GUEST EDITORS' INTRODUCTION: Testing inversion algorithms against experimental data: inhomogeneous targets
This special section deals with the reconstruction of scattering objects from experimental data. A few years ago, inspired by the Ipswich database [1–4], we started to build an experimental database
Reconstruction of Fine-Scale Structure of Acoustical Scatterer on Large-Scale Contrast Background
Strict mathematical methods of the solution of inverse problems are necessary for revealing a malignant pathology at the earliest stage of its growth, when the size of a disease area is a part of a millimeter.
Continuing with the Fresnel database: experimental setup and improvements in 3D scattering measurements
In this paper, the experimental setup and the improvements required to obtain further measurements for the third opus of the Fresnel Database are presented. The most original feature of those new